{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AF2XDKSGWA4D3NRPIIRO5QA6MI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9462d16a2bfb087f9c0783b0605753a050ff853a9c4c5f43c77eb9dec71cf6a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-02T17:32:31Z","title_canon_sha256":"6b4e6dc8b13a438d8559aa74cd0d42798b2f3fca8b3678b05b4f0fa0ac94cb87"},"schema_version":"1.0","source":{"id":"1901.00453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.00453","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1901.00453v1","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00453","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"AF2XDKSGWA4D","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AF2XDKSGWA4D3NRP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AF2XDKSG","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:bbaec2a8438c40591d34ee3b01eb79d70d84cba0831967b2a5d1ee85f0ffcd67","target":"graph","created_at":"2026-05-17T23:57:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the spectral asymptotics of nodal (i.e., sign-changing) solutions of the problem\n  \\begin{equation*} (H) \\qquad \\qquad \\left \\{\n  \\begin{aligned}\n  -\\Delta u &=|x|^\\alpha |u|^{p-2}u&&\\qquad \\text{in ${\\bf B}$,} \\\\\n  u&=0&&\\qquad \\text{on $\\partial {\\bf B}$,}\n  \\end{aligned}\n  \\right.\n  \\end{equation*}\n  in the unit ball ${\\bf B} \\subset \\mathbb{R}^N,N\\geq 3$, $p>2$ in the limit $\\alpha \\to +\\infty$. More precisely, for a given positive integer $K$, we derive asymptotic $C^1$-expansions for the negative eigenvalues of the linearization of the unique radial solution $u_\\alpha$ of $(H)$ ","authors_text":"Joel K\\\"ubler, Tobias Weth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-02T17:32:31Z","title":"Spectral asymptotics of radial solutions and nonradial bifurcation for the H\\'enon equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00453","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b753a4061ce6c2ec2a8e95915a8e4fb75a48ba72fd1bf072eb9cff4150bc7132","target":"record","created_at":"2026-05-17T23:57:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9462d16a2bfb087f9c0783b0605753a050ff853a9c4c5f43c77eb9dec71cf6a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-02T17:32:31Z","title_canon_sha256":"6b4e6dc8b13a438d8559aa74cd0d42798b2f3fca8b3678b05b4f0fa0ac94cb87"},"schema_version":"1.0","source":{"id":"1901.00453","kind":"arxiv","version":1}},"canonical_sha256":"017571aa46b0383db62f4222eec01e6223c29fcc7b274e14ca9490b3352a9db1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"017571aa46b0383db62f4222eec01e6223c29fcc7b274e14ca9490b3352a9db1","first_computed_at":"2026-05-17T23:57:03.811755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:03.811755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/AtdvHdWO8dHyF6ZRj2you0/yVFwMWHTxmuefIXeDGe0jwxk7DOLCIyC8Q33oAeoV19w3XCvsm4zhJwFhNc6Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:03.812389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.00453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b753a4061ce6c2ec2a8e95915a8e4fb75a48ba72fd1bf072eb9cff4150bc7132","sha256:bbaec2a8438c40591d34ee3b01eb79d70d84cba0831967b2a5d1ee85f0ffcd67"],"state_sha256":"3ad34ecec5c730d2cddf79aecc853bf1bc80c7f87b4cbbeab472463c955ec806"}